Finite Group Databasebeta

← #11776966

Subgroups — #11776966

Order 1152.

284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3792C211yesmaximal, characteristic
2#10591120C211yesmaximal, characteristic
3#10591066C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C2×#3792C412yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×#208—21no—
9#63777C411yescharacteristic
10#63777C411yescharacteristic
11C4×#622C2212yes—
12C3×#830—21no—
13#63572—21no—
14#63572C2211yescharacteristic
15#63572C2212yes—
16#63572C2211yescharacteristic
17#63555—21no—
18#5118—61no—
19#4719—61no—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3C2×C411yescharacteristic
22C22×C3⋊Dic3Q811yescharacteristic
23#3792—24no—
24C2×#622C2×C412yes—
25C2×#622C2×C412yes—
26C4×C3⋊Dic3C2×C411yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C4×C3⋊Dic3C2311yescharacteristic
30C3×#208—42no—
31C2×C3×C3⋊C8—22no—
32C2×C3×C3⋊C8—21no—
33C2×C3×C3⋊C8—21no—
34#1569—91nomaximal, Sylow
35C2×C3×M16—61no—
36C2×C4×Dic3—61no—
37C2×C4×Dic3—61no—
38C2×#208—21no—
39C3×C22⋊C8—61no—
40#830—21no—
41#815—61no—
42#815—61no—
43Dic3⋊C8—61no—
44Dic3⋊C8—61no—
45Dic3⋊C8—62no—
46Dic3⋊C8—62no—
47C23×C32C4⋊C411yescharacteristic
48C2×C32×C4—21no—
49C2×C32×C4—21no—
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C32×C4C2×D411yescharacteristic
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C2×C3⋊Dic3C22×C411yescharacteristic
57C2×C3⋊Dic3C2×Q811yescharacteristic
58#622—22no—
59#622M1614yescomplemented
60C3×C3⋊C8—41no—
61C3×C3⋊C8—42no—
62C3×C3⋊C8—41no—
63#432—91no—
64#423—91no—
65C4×M16—91no—
66#335—92no—
67#334—92no—
68C22×C3×C4—21no—
69C22×C3×C4—21no—
70C22×Dic3—61no—
71C22×Dic3—61no—
72C22×Dic3—61no—
73C22×Dic3—61no—
74C3×M16—122no—
75C2×C3×C8—62no—
76C2×C3×C8—61no—
77C2×C3×C8—61no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3—61no—
85C4×Dic3—61no—
86#208—42no—
87C2×C3⋊C8—22no—
88C2×C3⋊C8—21no—
89C2×C3⋊C8—21no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32C2×C4⋊C411yescharacteristic
94C32×C4—21no—
95C32×C4AGL(1,ℤ/8)11yescharacteristic
96C32×C4#13711yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—21no—
100C3⋊Dic3C2×M1612yes—
101C2×M16—61no—
102C2×M16—92no—
103C2×C42—91no—
104C4⋊C8—91no—
105C4⋊C8—92no—
106C4⋊C8—91no—
107C4⋊C8—181no—
108C22⋊C8—61no—
109#97—91no—
110#97—91no—
111#97—181no—
112C4×C8—92no—
113C23×C3—21no—
114C23×C3—21no—
115C2×C3×C4—22no—
116C2×C3×C4—22no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—41no—
122C2×C3×C4—41no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C2×Dic3—122no—
132C2×Dic3—122no—
133C2×Dic3—122no—
134C2×Dic3—122no—
135C3×C8—121no—
136C3×C8—121no—
137C3×C8—122no—
138C3⋊C8—41no—
139C3⋊C8—41no—
140C3⋊C8—42no—
141C2×C32—41no—
142C2×C32#42311yescharacteristic
143C2×C32#42811yescharacteristic
144C2×C32#43011yescharacteristic
145C22×C4—91no—
146C22×C4—91no—
147C22×C4GO+(4,𝔽2)11yescharacteristic
148M16—122no—
149M16—184no—
150C2×C8—61no—
151C2×C8—61no—
152C2×C8—62no—
153C2×C8—92no—
154C2×C8—92no—
155C42—91no—
156C42—91no—
157C42—91no—
158C42—91no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—21no—
162C22×C3—21no—
163C22×C3—41no—
164C22×C3—41no—
165C22×C3—41no—
166C22×C3—41no—
167C3×C4—22no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—41no—
173Dic3—62no—
174Dic3—62no—
175Dic3—62no—
176Dic3—121no—
177Dic3—121no—
178Dic3—121no—
179Dic3—121no—
180Dic3—121no—
181C32#156911yescharacteristic, complemented, Sylow
182C23#377311yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—182no—
190C2×C4—361no—
191C2×C4#377311yescharacteristic
192C2×C4C2×GO+(4,𝔽2)11yescharacteristic
193C8—94no—
194C8—122no—
195C8—121no—
196C8—121no—
197C8—182no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—42no—
205C2×C3—42no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22C2×#377311yescharacteristic
210C4—21no—
211C4—92no—
212C4—181no—
213C4—181no—
214C4—181no—
215C4#6423611yescharacteristic
216C4#6423911yescharacteristic
217C3—21no—
218C3—21no—
219C2—41no—
220C2#1059332811yescharacteristic
221C2#1059333011yescharacteristic
222C2#1059350711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1569
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #10590042C2semidirect
5. #10590041C2semidirect
59. #622M16semidirect
181. C32#1569semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#37922
#105911202
#105910662
#105900422
#105900412
#15699